JEE Main 2016 (2)

Algebra Level 4

Given that f(x)=x2px+qf(x)=x^{2}-px+q has has two prime numbers as roots and p+q=11p+q=11 where pp is an odd positive integer.

f(1)+f(2)+f(3)+f(4)++f(48)f(1)+f(2)+f(3)+f(4)+\cdots+f(48)

If the value of the above expression is AA, then find A1611\dfrac{A}{16}-11.


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